A long time asymptotic behavior of the free boundary for an American put

Authors:
Cheonghee Ahn, Hi Jun Choe and Kijung Lee

Journal:
Proc. Amer. Math. Soc. **137** (2009), 3425-3436

MSC (2000):
Primary 91B28, 35R35; Secondary 45G05

DOI:
https://doi.org/10.1090/S0002-9939-09-09900-6

Published electronically:
March 30, 2009

MathSciNet review:
2515412

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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we obtain a long time asymptotic behavior of the optimal exercise boundary for an American put option. This is done by analyzing an integral equation for the rescaled exercise boundary derived from the corresponding Black-Scholes partial differential equation with a free boundary.

**1.**Xinfu Chen; John Chadam,*A mathematical analysis of the optimal exercise boundary for American put options*, Siam J. Math. Anal.**38**, No. 5 (2006/07), 1613-1641. MR**2286022 (2007k:91131)****2.**Xinfu Chen; John Chadam; Lishang Jiang; Weian Zheng,*Convexity of the exercise boundary of the American put option on a zero dividend asset*, Math. Finance**18**, No. 1 (2008), 185-197. MR**2380946 (2008m:91109)****3.**Erik Ekstr m,*Convexity of the optimal stopping boundary for the American put option*, J. Math. Anal. Appl.**299**, No. 1 (2004), 147-156. MR**2091277 (2005f:91068)****4.**Jonathan Goodman; Daniel N. Ostrov,*On the early exercise boundary of the American put option*, Siam J. Appl. Math.**62**, No. 5 (2002), 1823-1835. MR**1918579 (2003i:35120)****5.**John C. Hull,*Options, Futures, and Other Derivatives*. 5th edition, Prentice Hall, NJ, 2002.**6.**A.M. Il'in; A.S. Kalashnikov; O.A. Oleınik,*Second-order linear equations of parabolic type*, J. Math. Sciences (New York)**108**, No. 4 (2002), 435-542. MR**1875963 (2003a:35087)****7.**S. D. Jacka,*Optimal stopping and the American put*, Math. Finance**1**, No. 2 (1991), 1-14.**8.**Robert C. Merton,*Continuous-time finance*, B. Blackwell, Cambridge, MA, 1990.**9.**R. M. Redheffer; W. Walter,*The total variation of solutions of parabolic differential equations and a maximum principle in unbounded domains*, Math. Ann.**209**(1974), 57-67. MR**0344683 (49:9422)****10.**Steven E. Shreve,*Stochastic calculus for finance. II. Continuous-time models*, Springer-Verlag, New York, 2004. MR**2057928 (2005c:91001)****11.**P. Wilmott; J. Dewynne; S. Howison,*Option Pricing: Mathematical Models and Computation*, Cambridge University Press, New York, 1995.

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Additional Information

**Cheonghee Ahn**

Affiliation:
Department of Mathematics, Yonsei University, Seoul 120-749 Korea

Email:
purehope@yonsei.ac.kr

**Hi Jun Choe**

Affiliation:
Department of Mathematics, Yonsei University, Seoul 120-749 Korea

Email:
choe@yonsei.ac.kr

**Kijung Lee**

Affiliation:
Department of Mathematics, Ajou University, Suwon 443-749 Korea

Email:
kijung@ajou.ac.kr

DOI:
https://doi.org/10.1090/S0002-9939-09-09900-6

Keywords:
American put option,
optimal exercise boundary,
free boundary problem

Received by editor(s):
April 30, 2008

Received by editor(s) in revised form:
November 27, 2008, and January 27, 2009

Published electronically:
March 30, 2009

Additional Notes:
The second author is supported by the Korea Research Foundation Grant funded by the Korean Government (MOEHRD, Basic Research Promotion Fund) KRF-2007-314-C00020.

The third author is supported by BK21 project of Department of Mathematics in Yonsei University (R01-2004-000-10072-0) and settlement research fund by Ajou University.

Communicated by:
Walter Craig

Article copyright:
© Copyright 2009
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.